Chapter 9. Growth through Technological Progress UMSL Max Gillman Max Gillman () 1 / 44
Facts: Positive Trend Growth Rate Ramsey (1928) World, economic growth assumed zero. in real GDP growth rate. "Classical": Ricardo, J.S. Mill, & Marx uses zero growth world. Also famous: Malthus (1798) Essay on Principle of Population, population will grow so as to keep per-capita output constant (no growth). Ramsey’s (1928) in line with trend growth rate experience, at the time Industrial revolution started in Great Britain around 1750’s, with positive growth now normal in developed economies. Brought about rethinking of facts of economy. With growth in real GDP, growth in real consumption and in real investment had to keep pace real GDP. This way have stable shares of cons. & inv. in GDP. So add: that growing variables all grow at same rate. Max Gillman () 2 / 44
Stylized Growth Rate Facts 1: output grows at some steady rate. 2: All variables that grow over time grow at same rate as GDP output: output y , consumption c , investment i , & capital stock k & wage w . Gives the trend growth rate of economy. Trend growth rate depends on time period and country. 2% commonly used for US past century; 3.5% US Post-1959. Europe & Japan; developed countries similar growth trend to US. Max Gillman () 3 / 44
Europe, Japan, US Post WWII Growth Rates Figure: Real GDP Growth Rate, annual basis, for Four Industrial Nations Plus the Euro-zone Countries. Max Gillman () 4 / 44
Solow Growth Facts Stylized growth facts explained by Solow. Solow starts with constant growth rate, such as 2%. Adds real wage growing over time. Real interest rate stable over time. Rising real wage goes with rising per capita income. Stable real interest rate goes with output to capital ratio being constant. Uses theory of marginal products of capital & labor. Marginal product of capital is set fraction of y / k : so output to capital ratio is constant since Real interest rate equals marginal product of capital. Real wage is Marg Product of labor=fraction of y / l . So y / l growing implies w growing. Max Gillman () 5 / 44
Given Constant Output Growth Rate: 4 facts Real wage w rises steadily over time at real output growth rate. 1 Real interest rate r remains constant on average over time. 2 Per capita income, or output divided by total labor supply, rises at 3 same output growth rate. Output to capital stock ratio remains constant on average over time. 4 Max Gillman () 6 / 44
Harberger & Falling Relative Cost of Output Harberger (1998) argues: real cost of goods falls over time due to Solow-type technological progress. Harberger says "real cost reduction" lowers percent of real GDP used up in production. Capture this is by comparing Ramsey-Solow cost of goods (and capital) relative to labor. Steady technological progress makes real price of good relative to labor lower over time (Harberger, 1988). CPI index divided by the nominal wage rate gives real relative price of goods to labor, so 1 / w should fall over time. Rise of real wage over time, one of Solow’s Facts, automatically gives fall of real price of goods relative to labor over time. Max Gillman () 7 / 44
Solow Plus Growth Facts The relative price of output to labor falls over time. 1 Real price of output relative to labor, 1 / w , falls over time. 1 Is satisfied if Solow Growth Facts are met, as include rising wage w . 2 Average hours worked per week very gradually decrease. 2 Time spent in education steadily rises over time. 3 Time spent for leisure falling over time. 4 Max Gillman () 8 / 44
Theory: Zero Growth to Positive, Constant, Growth Allow for exogenous technological progress. Stated in terms of productivity parameter of output production function that increases at constant rate over time. Causes variables to grow at constant growth rate. Just assume but do not explain productivity increase. May say progress due to research & development, to human capital accumulation, or rising aggregate "knowledge". Model known as exogenous growth model . Simple extension of Ramsey World to Ramsey-Solow World. Productivity parameter A now rises at steady rate. "Solow Growth theory": explains 4 stylized Solow growth facts. Max Gillman () 9 / 44
Facts along a Balanced Growth Path Equilibrium Equilibrium called "balanced growth path" equilibrium . output, consumption, investment & capital all grow at same rate. To explain business cycles: used changes in two parameters, output productivity & time endowment. Interpreted these changing two main resources: goods & time endowments. Apply same two " comparative static " changes for growth process. Productivity increase used to explain 4 Solow growth facts. Time endowment change added to productivity increase to explain additional 4 Solow Plus growth facts, while maintaining original four Solow growth facts. Max Gillman () 10 / 44
Growth Puzzle that Solow Solved All variables growing at same rate raises question: How can output grow if labor cannot. Labor constrained by stationary, or constant, time endowment. If labor share of time continually grows, no leisure time left. consumer would not choose to allow this. If capital alone grows, with labor constant, then marginal product of capital gets increasingly small. Follows from diminishing product of labor: Adding more capital causes smaller increase in output. Diminishing marginal product: no constant rate of growth in output unless capital grows exponentially. But faster capital growth than output growth inconsistent with balanced growth equilibrium. Also inconsistent with Growth fact: constant output to capital ratio. Problem solved by Solow with "augmented-labor" & capital inputs growing by same amount, with productivity parameter growth "augmenting" labor. Max Gillman () 11 / 44
A Comparative Static Productivity Increase C omparative static change of Solow’s Growth theory is increase in productivity. Here illustrate this initially with single 5 % increase in production function productivity parameter A . Causes marginal productivity of both labor & capital to increase. Marginal cost of goods falls, AS curve shifts out: more output supplied for each relative price 1 / w . Higher wage from higher marginal product of labor, consumer gets more capital wealth & increases demand for consumption; AD curve shifts out. "Supply Side Economics": AS shifts out by more than AD ; falling 1 / w . Max Gillman () 12 / 44
Productivity Increase Shifts Out AS & AD 15 1/w 10 5 0 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 Aggregate Output y Figure: AS − AD Equilibrium with Goods Productivity Increase (in Black) as Compared to the Original (in Red). Max Gillman () 13 / 44
Productivity Change Effect on Labor Market Labor market: demand shifts out for labor because higher marginal productivity of labor. Supply shifts back because consumer has higher capital wealth k , so unwilling to work as much at any given wage rate. Net effect: equilibrium quantity of labor unchanged, consumer working same amount of time, while real wage rises. Max Gillman () 14 / 44
Real Wage Up, Employment Unchanged 0.30 w 0.25 0.20 0.15 0.10 0.05 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 Labor Employment Figure: Increase in Productivity (Black Curves) Raises w and Leaves Employment Unchanged. Max Gillman () 15 / 44
Real Interest Unchanged, Investment Up Capital market: marginal product of capital rises & demand for capital shifts out while interest rate remains fixed (at 6% in the example). Equilibrium capital k & investment ( δ k ) rise. Fixed r because of exogenous growth assumption. Interest rate fixed in equilibrium by assumed growth rate: this is fact of Ramsey-Solow Exogenous growth theory. Note: With extension to human capital, productivity rise is endogenous, as is growth rate, & real interest rate is not fixed. Max Gillman () 16 / 44
Productivity Change Effect on Capital Market 0.10 Real Interest Rate r 0.09 0.08 0.07 0.06 0.05 0 1 2 3 4 5 Capital Stock k Figure: Capital Market Shows Shift Out of Demand for Capital (Black Curve) When Factor Productivity A Increases 5 % from Original value (Red Curve). Max Gillman () 17 / 44
Productivity Effect on Utility & Production Consumption & output rise by same amount so "propensity to consume", or conversely savings rate, remain same. Here consumption rate is two-thirds: c / y = 0 . 67 Production function pivots up; utility level rises, indifference curve shifts up. Budget line actually pivots upwards, since its slope rises: w / r is slope & w rises, r stays same. Labor employment unchanged at 0.5 . Max Gillman () 18 / 44
Productivity Pivots Up Production Function 0.22 c Consumption 0.20 0.18 0.16 0.14 0.12 0.10 0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 l Labor Figure: General Equilibrium Production, Utility Levels and Budget Lines with Goods Productivity Increase (Darker Curves) Compared to Baseline (Lighter Curves). Max Gillman () 19 / 44
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